Mhaskar has recently proposed the first wavelet-type frame construction for functions defined on directed graphs [1]} as an extension of the diffusion polynomial frames [2]}. Although our redundant wavelet construction on directed graphs is inspired in part by that of polynomial diffusion frames, it differs mainly in the choice of the Fourier basis and the considered operator. Mhaskar proposes in [1]} the set of left-singular vectors of the weighted adjacency matrix of a directed graph as a Fourier basis while we propose the set of eigenvectors of the random walk operator.
